1478 Integr. Biol., 2012, 4, 1478–1486 This journal is c The Royal Society of Chemistry 2012

Cite this: Integr. Biol., 2012, 4, 1478–1486

Inter-cellular signaling network reveals a mechanistic transition in tumor

microenvironmentw

Yu Wu,aLana X. Garmire

bcand Rong Fan*

ad

Received 29th February 2012, Accepted 4th October 2012

DOI: 10.1039/c2ib20044a

We conducted inter-cellular cytokine correlation and network analysis based upon a stochastic

population dynamics model that comprises five cell types and fifteen signaling molecules inter-

connected through a large number of cell–cell communication pathways. We observed that the

signaling molecules are tightly correlated even at very early stages (e.g. the first month) of human

glioma, but such correlation rapidly diminishes when tumor grows to a size that can be clinically

detected. Further analysis suggests that paracrine is shown to be the dominant force during tumor

initiation and priming, while autocrine supersedes it and supports a robust tumor expansion. In

correspondence, the cytokine correlation network evolves through an increasing to decreasing

complexity. This study indicates a possible mechanistic transition from the microenvironment-

controlled, paracrine-based regulatory mechanism to self-sustained rapid progression to fetal

malignancy. It also reveals key nodes that are responsible for such transition and can be

potentially harnessed for the design of new anti-cancer therapies.

It has been increasingly recognized that tumor cells do not

develop in isolation, but actively interact and co-evolve with

stromal cells via a complex inter-cellular signaling network.

For example, glioblastoma multiforme (GBM),1 the most

malignant human brain tumor, consists of a highly hetero-

geneous mixture of cell types including activated astrocytes

and microglia. These cells play a crucial role in tumor initiation,

progression and invasion.2 They interact with glioma and

glioma stem cells through either direct cell–cell contact or

soluble protein-mediated signaling pathways. Neglecting the

inter-cellular interaction network in tumor microenvironment

is inappropriate for comprehensive understanding of tumor

development and implicated in the failure of many anti-cancer

therapies. A systems biology approach is highly desired to

investigate complex tumor microenvironment and recapitulate

in vivo dynamical evolution of a tumor. Towards this goal,

several approaches have been proposed to model tumor

development,3–7 and these mathematical models have significantly

advanced our understanding of tumor microenvironment.8,9

Discrete dynamical systems are employed to describe cell

proliferation, differentiation and death.10,11 Continuous, agent

based and hybrid tissue level models have been developed in

aDepartment of Biomedical Engineering, Yale University, New Haven,CT 06511, USA. E-mail: rong.fan@yale.edu

bAsuragen, Inc., Austin, TX 78744, USAcUniversity of Hawaii Cancer Research Center, Honolulu, HI 96813,USA

dYale Comprehensive Cancer Center, New Haven, CT 06520, USAw Electronic supplementary information (ESI) available. See DOI:10.1039/c2ib20044a

Insight, innovation, integration

Tumor cells do not develop in isolation, but actively interact

and co-evolve with stromal cells via a complex inter-cellular

signaling network. Although the role of individual stromal cells

or soluble mediators has been investigated, a systems-level

picture showing the collective effect of cellular and molecular

components in tumor microenvironment is yet to be realized.

Here we exploit an integrative model that recapitulates the

complex cell–cell communication network in human brain

tumor microenvironment to assess the collective behavior of

inter-cellular signaling pathways. We observed a sharp change

of cytokine correlation network during tumor development

indicative of a possible mechanistic transition from the

microenvironment-controlled, paracrine-based regulatory

mechanism to self-sustained rapid progression to fetal

malignancy. It also reveals key nodes that are responsible

for such transition and can be potentially harnessed for the

design of new anti-cancer therapies. Finally, this study can

serve as a generic approach to integrate experimental data

and reveal underlying mechanisms of tumor microenviron-

ment at the systems level.

Integrative Biology Dynamic Article Links

www.rsc.org/ibiology PAPER

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This journal is c The Royal Society of Chemistry 2012 Integr. Biol., 2012, 4, 1478–1486 1479

attempt to assess selected aspects of tumorigenesis such as

tumor heterogeneity, selective pressure imposed by physical/

chemical conditions of extracellular matrix, phenotypic change

triggered by intracellular gene–protein interaction, and growth

dynamics.12–19 Probabilistic models are used to examine the

mechanism of mutation-driven tumorigenesis.20–23 Although a

variety of mathematical modeling strategies have been reported,

population dynamics modeling using a set of differential equation

best suits the study of tumor development and progression.

Ordinary differential equation (ODE) models have been formu-

lated to analyze dynamical evolution of human tumors, such as

prostate cancer development with anti-androgen therapy in an

intermittent manner,24 stability and bifurcation analysis in tumor

gene regulatory network,25 feedback loops in stem cell driven

carcinogenesis,14,26 p53 bistability dynamics,27 Myc-p53 regulation

system of cell proliferation and differentiation,28 fitness and selec-

tion in a history formulation,29 multistep mutation transformation

to cancer,30 and cell cycle transition in cancer cells.31 Partial

differential equation (PDE) models have also been well established

to study problems involving multiple variables, like spatial

dimensions, and thus represent a favorable method to inves-

tigate metastatic invasion,32–34 tumor angiogenesis,35 and the

dynamics of intra-tumoral convection or diffusion.36,37 Differ-

ential equation-based approaches are also capable of modeling

the co-evolution of tumor cell and microenvironment.38–40 For

example, tumor-fibroblast crosstalk via two signaling proteins

TGF-b and EGF was studied using a partial differential equation

model and the result was found to be good agreement with in vitro

tumor model created on a semi-permeable membrane.41,42

While most studies concern only a few selected signaling path-

ways in a tumor, we have developed the first model to study the

co-evolution of tumor and stromal cells at a large scale and the

systems level.43 Herein, based upon this model, we conducted the

analysis of cytokine correlation and inter-cellular signaling network

in human glioblastoma to assess the collective role of cytokine

network in regulating tumor–tumor microenvironment inter-

actions. This model comprises five types of cells, fifteen signaling

proteins and 69 signaling pathways (Fig. 1). The in silico results,

which are entirely derived from the stochastic simulations without

fitting to the experimental data, reflect many emerging patterns and

observations that are consistent with human glioma development.

Most importantly, we observed the change of cytokine correlation

that reveals a rapid transition from the microenvironment-

controlled, paracrine-based regulatorymechanism to self-sustained,

autocrine-dominant progression to malignant states. We detail the

findings and merits of such findings in the following.

Results

Construction of a cell–cell communication network in human

glioma microenvironment

The population dynamics model of glioblastoma microenviron-

ment has been described previously.43 To help understand the

Fig. 1 Intercellular signaling network in human glioblastoma microenvironment. (a) Schematic depiction of human glioblastoma. (b) Flow chart

showing the construction of a quantitative ODE model of intercellular signaling network. (c) Detailed depiction of inter-cellular signaling network

in human glioma microenvironment. QSC, quiescent glioma stem cell. ASC, activated glioma stem cell.

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1480 Integr. Biol., 2012, 4, 1478–1486 This journal is c The Royal Society of Chemistry 2012

further analysis of inter-cellular cytokine network and the

approach toward the discovery of new biological insights, here

we briefly re-describe the basic principles and governing equations

of this model. The model integrates population dynamics and

Hill functions to describe soluble protein-mediated inter-cellular

signaling network in tumor microenvironment. This was realized

using a coupled stochastic population dynamics model. The

evolution of signaling network is interpreted by population

dynamics, so the concentration of cells/signaling molecules are

controlled by a set of stochastic ordinary differential equations.

The details of all ODEs we constructed, their biological implica-

tion, and the references from which input values were derived are

summarized in full detail in ESI.w The general mathematic

representation is

is the angiogenesis factor (Fig. S1(a), ESIw). Monte Carlo

simulations of one year evolution under such parameter settings

show that glioma cells evolve through three distinct phases, the

pre-tumor phase (1–5 months), the rapid expansion phase (6–10

months), and the malignancy phase (11–12 months) (Fig. 2(a)).

The three-phase dynamics is demonstrated by our model and

consistent with glioblastoma development observed in animal

models.44 The longest period is the pre-tumor phase, which

is the stage of accumulate genetic and microenvironmental

prerequisites to initiate neoplastic transformation. In the context

of human glioma, if a tumor microenvironment imposes an

evolutionary selection towards astrocytes, the neoplastic process

may be halted or even reversed by the increasing apoptotic

rates of abnormal/neoplastic cells. The abnormal/neoplastic

cells that have survived in the pre-tumor phase gradually gain

fitness advantage over astrocytes, and further progress to

rapid expansion phase mathematically characterized by a

typical exponential growth mode. The tumor cells increase in

frequency over time and eventually become the most abundant

population. However, the crowded tumor cells compete for

resource and, if confined in a given volume, will approach an

equilibrium state with a large mass of tumor, which is defined

as the malignancy phase.

Since the tumor cells and microenvironment co-evolve in a

gradual and continuous manner, there is no distinct boundary

between adjacent phases. In this study, we use the following

rules to calculate the length of three phases and the results are

rounded to the nearest month. First, the boundary between

pre-tumor phase and expansion phase is the time point when

the tumor cell proliferation enters the typical exponential

growth mode and achieve a moderate density, but still below

the theoretical detection limit of MRI (10 labeled cells per

100 mm3 volume45) and enhanced CT (40 000 cells per cm2 46).

Second, the boundary between expansion phase and malignancy

phase is the time point where tumor cells deviate from the

exponential growth trajectory. Afterwards, tumor cells enter a

saturated logistic growth mode and the tumor cell population is

close to 95% of equilibrium.

dxi

dt

z}|{rate of change ofcell concentration

¼XNiðtÞ

k¼1Ykdðt� tkÞ

zfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflffl{immigration; emigration;differentiation from progenitor

þ riðtÞxi 1� xi

ximaxaangiogenesis

� � YNcytokine

l¼1

YNcytokine

m¼11þ uilðtÞyl

sl þ yl

� �1� fim þ

fimsm

sm þ ym

� �zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{proliferation

� dixiYNcytokine

n¼11� gin þ

ginsn

sn þ yn

� �zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{decay

þXNcell

k¼1mikðtÞxk

YNcytokine

p¼11� hip þ

hipyp

sp þ yp

� �zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{mutation; differentiation;dedifferentiation from cell xk

ð1Þ

dyj

dt

z}|{rate of change ofcytokine concentration

¼XNcell

k¼1kjkðtÞxk

YNcytokine

l¼1

YNcytokine

m¼1

YNcytokine

n¼11þ ujlðtÞyl

sl þ yl

� �1� vjm þ

vjmym

sm þ ym

� �1� wjn þ

wjnsn

sn þ yn

� �zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{production from cell

� mjyjYNcytokine

p¼11þ ujpyp

sp þ yp

� �zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{decay

ð2Þ

i = 1, . . ., Ncell j = 1, . . ., Ncytokine

where

aangiogenesisðtÞ ¼ 1þ ucell IL1yIL1

sIL1 þ yIL1

� �1þ ucell VEGFyVEGF

sVEGF þ yVEGF

� �1þ ucell HGFyHGF

sHGF þ yHGF

� �1þ ucell MIFyMIF

sMIF þ yMIF

� �

1þ ucell SCFySCF

sSCF þ ySCF

� �1þ ucell FGFyFGF

sFGF þ yFGF

� � ð3Þ

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Population dynamics of cells and cytokines in glioma

microenvironment

Among the five types of cells included in the modeling,

glioma, microglia and ASC all show population increase,

whereas astrocyte and QSC present a continuous depletion

of population (Fig. 2). Glioma has the most drastic sigmoid-

shaped growth among all (Fig. 2(a)). Microglia shows com-

paratively marked increment, reflecting an active role in the

development of GBM (Fig. 2(b)). QSC upon stimulation

undergoes a reversible process to be activated into ASC

conferring self-renewal capability. Under the initial conditions

of the model, it favors activation direction, thus QSC

continuously decreases in sizes (Fig. 2(d)) to give rise to

ASC (Fig. 2(e)). To reveal the underlying cell fate and the

switch of tumor phases, we also use ‘‘fitness’’ to represent per

capital growth rate:

FiðtÞ ¼dxi=dt

xi; i ¼ 1; . . . ;Ncell ð4Þ

Glioma, microglia and ASC all show positive fitness,

with Glioma maintaining the highest order of fitness

(Fig. 2(a, b, and e)). Tightly following the initial expansion

phase of tumor, all three cells have sharp peaks in fitness. The

decline of fitness curves at the end of sixth month is due to the

density-dependent effect as the population approaching the

carrying capacity. As the cells compete for nutrition, the ones

acquire relatively high fitness gain superiority at the price of

others, thus QSC and astrocyte score negative fitness values,

accompanying the continuously decreasing population

(Fig. 2(c and d)). Though being infiltrated by tumor cells,

astrocytes strive for keeping abundance until their throne is

usurped by glioma due to accumulated tumorigenic agents

(Fig. 2(c)).

Autocrine to paracrine transition in tumor development

Glioma cells do not develop in isolation, but co-evolve

with stromal cells in tumor microenvironment mediated by

autocrine/paracrine signaling network. A specific intercellular

signaling could be either autocrine or paracrine depending on

their secretion source. To reflect the effect of autocrine and

paracrine, we define ‘‘autocrine to fitness index’’ (eqn (4)) and

Fig. 2 Stochastic dynamics and fitness evolution of glioma, microglia, astrocyte, QSC, and ASC, respectively. The different grayscale zones

represent three distinct phases of glioma development revealed by the dynamics modeling; they are pre-tumor phase (white), expansion phase (light

gray), and malignancy phase (dark gray). The blue solid curves are the stochastic dynamics of cells, whereas the red dashed lines represent the

evolution of fitness, defined as per capita cell growth rate.

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‘‘angiogenesis factor (eqn (3)) with the autocrine indices’’ as

follows:

i = 1, . . ., Ncell

We define ‘‘paracrine index’’ Pi(t*, Dt) and the ‘‘total

intercellular signaling index’’ Ti(t*, Dt) similarly. The one year

simulation of Afitnessglioma, Aangio

glioma, Pfitnessglioma, Pangio

glioma, Tfitnessglioma, and

Tangioglioma are shown in Fig. S1(b–d) (ESIw). Paracrine contributes

to the major part of glioma fitness and angiogenesis in the pre-

tumor phase. However, it is gradually substituted by autocrine

since the expansion phase. The breakdown of the driving force

facilitates examining the contributions of all the paracrine/

autocrine loops associated with tumor development, therefore

we calculate the ‘‘proportion of autocrine’’ by the following

definition

Aiðt�;DtÞTiðt�;DtÞ

ð7Þ

We show the proportional contribution of autocrine and paracrine

in Fig. 3. The results surprisingly suggest a rapid but smooth

transition from paracrine-driven to autocrine-driven tumor

progression. Glioma is initiated and primed in a paracrine

condition, thus in the pre-tumor and early expansion stage, its

fitness is significantly dependent on the microenvironment.

However, once the paracrine-triggered tumor progression enters

mid-expansion phase, the accumulated autocrine signaling

replaces paracrine and the tumor progression will be resistant

to interventions from the microenvironment.

It is of interest to investigate how paracrine loops are

established and promotes tumorigenesis. We further break-

down the paracrine driving force and classified them according

to their source cell type. The results shown in Fig. S2 (ESIw)demonstrate heterogeneity in paracrine contributors. For example,

microglia and astrocyte are the major paracrine donors of glioma

fitness at the very beginning. However, their effects turn

negative at the end of the sixth month, while the ASC starts

to make positive paracrine contribution to glioma fitness. The

heterogeneity stems from the fact that autocrine and paracrine

do not evolve in isolation, but actually nonlinearly coupled via

feedback loops in the complex cell–cell communication network

(Fig. 1). This observation suggests that the microenvironment-

specific anti-cancer therapy is likely to hit a moving target, and

its success requires a careful study of evolution of the inter-

cellular molecular network due to such intervention.

Cytokine correlation map reveals active cell–cell communication

and also exhibits an abrupt transition

Signaling molecules are interwoven into complex networks.

They work in concert to achieve intercellular communication

and regulate cell behaviors. To assess the heterogeneous

behavior of signaling molecules and the association with tumor

development, we design a correlation matrix analysis – at a

given time, the concentration of the signaling molecule, x, is

perturbed by �Dx; the resulting concentration change of

another signaling molecule, y, after 72 hours is Dy+ and Dy�,corresponding to perturbing +Dx and �Dx, respectively. Thecorrelation factor cx-y is defined as

cx!y ¼ðyþDyþÞ�ðyþDy�ÞðyþDyþÞþðyþDy�Þ

að8Þ

where a = Dx/x.The influence of a signaling molecule on the other is

quantitatively defined by a correlation factor. Experiments

over all these signaling molecules yield a heat map of correla-

tions, also called the correlation matrix (Fig. 4). Each row of

the matrix represents the responses of all signaling molecules

including itself upon a signal perturbation experiment, at a

given simulation time. The snap-shot heat-map results indicate

these signals are indeed interlinked and the perturbation of

one may significantly influence the production of the other

signaling molecules, presumably via cells as the nodes. More

importantly, the time course of signaling correlation network

(Fig. S3, ESIw) exhibits a striking dynamic behavior that

cannot be easily revealed by the collective behavior shown in

Fig. 3. Substantial correlations between a number of signaling

Fig. 3 The evolution of the driving force for glioma progression. The

paracrine signaling is the dominant force during the pre-tumor stage,

while autocrine signaling becomes the major driving force in the

expansion and malignancy phases. The transfer of leadership results

in the significant enhancement of the robustness of tumor in a self-

sustained manner.

Afitnessi ðt�;DtÞ ¼ Fautocrine

i � F zeroi ¼ dxi=dt

xi

����xj¼x�j þx

autocrinej

;yk¼y�kþyautocrinek

;t¼t�þDt�dxi=dt

xi

����xj¼x�j þx

zeroj

;yk¼y�kþyzerok

;t¼t�þDtð5Þ

Aangioi ðt�;DtÞ ¼ aautocrineangiogenesisðt�;DtÞ � azeroangiogenesisðt�;DtÞ ¼ aangiogenesis

���yj¼y�j þy

autocrinej

;t¼t�þDt�aangiogenesis

��yj¼y�j þy

zeroj

;t¼t�þDt ð6Þ

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molecules emerge at a very early stage (month 1) and become

much greater during the period of rapid glioma expansion

(month 6), but quickly diminish when the tumor reaches a

steady state (month 7–12). Also the correlation pattern

changes drastically along the course of tumor development

(Fig. S4, ESIw). For example, many factors (such as SCF)

negatively regulate TGF-b, EGF and VEGF in the first month,

but turns to positively modulate these signaling molecules in the

sixth month when glioma cells reach the rapid expansion stage.

On the other hand, MCP1, which appears independent of any

other signaling molecules in the early and mid stages, is the only

cytokine that remains actively interacting with other signaling

molecules in the late stage. Such striking pattern switch implies

that therapeutic intervention that targets cytokine signaling need

to be executed at the early or mid stages when they are inter-

linked, whereas such treatment at a slightly late stage may not

show efficacy due to the diminishment of cytokine regulatory

network. We further analyzed the evolution of signaling correla-

tion pattern (Fig. S4, ESIw). The signaling correlations

were found to be in cooperation (e.g. IL-6 and EGF at the

sixth month47,48), competition (e.g. IL-1 and PGE2 at the sixth

month), or equilibrium (e.g. IL-10 and TNF-a at the sixth

month) (Fig. S5, ESIw), reflecting their different regulatory

functions in the tumor microenvironment.

Cytokine network identifies key nodes in dictating tumor

development

While heat-maps convey overall impressions of the correlation

matrix, reconstructed correlation networks may reveal encoded

connections more directly. The fifteen signaling proteins can be

classified into five sub-sets according to their cellular function;

these subsets are growth factors (EGF, VEGF, HGF, FGF,

and SCF), proinflammatory cytokines (IL-1, IL-6, and TNF-a),anti-inflammatory cytokines (IL-10, TGF-b), chemokines

(MCP-1, MIF, GCSF, and GMCSF) and Prostaglandin E2.

Perturbation on one signaling molecule will exert regulatory

effect on the others via intercellular signaling network. We

define the impact factor, the capability of one signaling mole-

cule to regulate others and change the network topology, as the

sum of the correlation factors:

Ii ¼XNcytokine

j¼1cij; i ¼ 1; . . . ;Ncytokine ð9Þ

To deliver a global view of the intra- and inter-group signaling

regulation, we construct a correlation network (Fig. 5), which

integrates concentration, impact factors, and the directional

connections of signaling molecules. The time evolution of

correlation network reveals several interesting findings (Fig. S6,

ESIw).

Fig. 5 Evolution of correlation network of signaling molecules in

five functionally classified sub-sets, including growth factors (purple

circle), proinflammatory cytokines (green), anti-inflammatory cyto-

kines (cyan), chemokines (magenta), and PGE2. Each blue circle

(node) represents a signaling molecule. The diameter of the node is

proportional to the concentration of the molecule, and the color

indicates the impact factor of the cytokine according to the blue color

bar. The arrow link between two nodes represents the directional

regulation of the two signals. The green-red color bar shows the

strength of the up-regulation (red) and down-regulation (green).

Fig. 4 Signaling correlation matrices. Heat maps show the signaling

correlation matrices at selected times. A profound intercellular signaling

correlation emerges at the very early stage (month 1), but almost

diminishes as soon as the tumor development enters the rapid expansion

phase (month 6).

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1484 Integr. Biol., 2012, 4, 1478–1486 This journal is c The Royal Society of Chemistry 2012

Firstly, in the first three months, the growth factor, proin-

flammatory and anti-inflammatory cytokine groups have unilateral

regulation on the chemokine group. There is no mutual effect

between the former three groups until the fourth month, exhibited

by the growth factor – pro-inflammatory cytokine and the growth

factor – anti-inflammatory cytokine connections. The chemokine

group gradually strengthens its influence, and becomes the sole

dominant inter-group connector in the late expansion phase and

malignancy phase. The observation suggests that the signal net-

work is not random, but orderly organized and coordinates with

cytokine function. Secondly, there is no necessary link between the

impact factor and concentration. The cytokine with high plasma/

cerebrospinal fluid concentrationmay not have significant influence

on the intercellular signaling network, suggesting acquiring of

expression level at only one time point can not reflect dynamic

trend and may lead to misjudgment. Thirdly, the dynamic

processes evolve fast in the pre-tumor and expansion phase,

and become stable in the malignancy phase. Drastic changes are

observed in the fifth to seventh months. This process is in line

with the establishment of tumor robustness.

Discussion

We constructed a large-scale, intercellular signaling network in

brain tumor microenvironment that includes major cell types and

important signaling molecules related to the tumorigenesis events.

A stochastic population dynamics model is used to recapitulate

the co-evolution of tumor and tumor microenvironment. The

model enables the quantification of tumor fitness and unveils the

underlying mechanism driving tumor progression. Without fitting

to experimental data, this fully predicable model yields emerging

patterns that are consistent with experimental observations,

demonstrating its merits in physical sciences of cancer.

One of the most important findings is the gradual change of

dominant signaling from paracrine to autocrine that starts from

the tumor expansion phase to the malignancy phase in which

glioma cells become self-sustained and auto-driven. This agrees

well with recent studies showing cooperative cell–cell interaction-

induced tumorigenesis48,49 and epithelial–mesenchymal transition

in tumor development.50 More importantly, the model serves as a

tool to study the fundamental questions in respect to the role of

tumor microenvironment by perturbing this system one molecule

at a time and examining the collective responses accordingly.

The metrics of correlation matrix was developed to analyze

the intercellular signaling network and we observed a striking

mechanistic transition: the signaling network emerges at the very

early stage, peaks at the mid stage of expansion, but quickly

diminishes when the tumor grows to a clinically-detectable size

(1 � 106 ml�1).45,46,51 Further analysis suggests that paracrine

represents a dominant force during tumor initiation and priming,

while autocrine supersedes it and supports a robust tumor

expansion. Network analysis of all five functional clusters

identifies the key nodes responsible for such change. All these

studies indicate a possible mechanistic transition from the micro-

environment-controlled, paracrine-based regulatory mechanism

to self-sustained rapid progression to malignancy stages.

The proposed modeling method and protein correlation

analysis provide a mathematic framework to study the dynamics

of multi-cellular systems and protein correlation network.

Therefore it should be able to be generalized and applied to

other disease systems, which involve heterogeneous cellular

environment and communication network. The current modeling

results also provide new insights into the design of personalized

therapy. While most anti-cancer therapeutic strategies focus on

direct targeting of cancer cells, this study suggests an alternative

approach that targets the microenvironment of a tumor. To

utilize the current model to design therapy, there are two major

steps. First, evaluate the dynamic protein levels and determine all

the potential targets that can maximize the efficacy and minimize

the side effects; Second, perturbation analysis to examine the

effect of deleting or enhancing these potential targets in a

combinatorial fashion. To do so, we have utilized a sensitivity

analysis to assess the effect of multiple signals on tumor cell

growth rate.43 The most dominant signals can be identified by

changing one factor at a time, and the synergistic effect can be

revealed by perturbing multiple factors simultaneously to infer

the design of combination therapy. It is also worth noting that

the sensitivity analysis can be performed over the entire time

course to longitudinally assess the changing effect of perturba-

tions on the whole system. As shown in Fig. 3, the one that

contributes the most to tumor fitness in pre-tumor phase belongs

to paracrine signaling, while in later stages it changes to autocrine

signaling. Therefore, this modeling approach not only provides

the targets for therapeutic intervention but more importantly the

timing of treatment. When the model is applied to monitoring of

patient response, the levels of proteins and cell populations can

be quantified by measuring clinical tumor specimens. The results

can be fed into the model such that it becomes individualized and

can predict targets for the specific patient. Once the model is

trained with clinical data, it could become a tool to guide the

therapy and predict outcomes on the individual patient basis.

Materials and methods

Assumptions and model construction

A well-mixed species system is considered to capture the time

evolution of tumor. We assume that the species included in the

model evolve independently of species excluded from the model

(oligodendrocyte, etc.). The regulatory effect of cytokines to cell

proliferation is expressed by Hill functions.52 The stochastic

parameters in eqn. (1) and (2) are

riðtÞ ¼ r0i 1þ e sin2pr0iln 2

tþ bWðtÞ þ D� �� �

; eo 1 ð10Þ

mikðtÞ ¼ m0ik 1þ e sin

2pr0kln 2

tþ bWðtÞ þ D� �� �

;

0 � m0ik � 1; 0 � e � min 1;

1

m0ik

� 1

� � ð11Þ

kjk(t) = k0jk max (0,1 + sx(t)) (12)

uil(t) = u0il max (0,1 + sx(t)) (13)

ujl(t) = u0jl max (0,1 + sx(t)) (14)

ujp(t) = u0jp max (0,1 + sx(t)) (15)

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This journal is c The Royal Society of Chemistry 2012 Integr. Biol., 2012, 4, 1478–1486 1485

where W(t) is a standard Wiener process, and x(t) is a zero-

mean Gaussian white noise with unit intensity.

Monte Carlo simulation

The stochastic dynamics are studied using Monte Carlo

simulations. The eqn (1) and (2) have been integrated using

both routine ode4 (fixed-step classical fourth-order Runge–

Kutta schemes) with Matlab code and solver ode45 (variable-

step Dormand–Prince 4–5 pair method) in Simulink modules.

The fixed step size for ode4 is 0.01, and the relative error

tolerance for ode45 is 1 � 10�6. They gave almost the same

results. The generation of Gaussian and Poisson white noise in

eqn (1) and (2) are involving employing of functions randn and

poissrnd, respectively. The Wiener process in eqn (10) and (11)

is further generated by integrating Gaussian white noise.

Parameter selection

We tried our best to identify all input values or ranges from

published experimental data. However some parameters are

still unavailable to our best knowledge. We have to make the

best estimation based on indirect experimental observations or

related studies. Other parameters, for example, the activation/

deactivation rates of stem cells, are highly dependent upon the

exogenous stimuli, thus could vary in a quite wide range.

However we would argue that the initial settings of many

parameters only change the quantitative timeline of the dynamics

but would not affect the general trends observed in our model

that properly reflect the dynamics of human glioma. Thus,

without the loss of generality we assigned moderate values to

these parameters. We also calibrated our model by adjusting the

Hill function parameter scytokine and matching the simulation to

published in vitro dynamics data.

For further discussion and analysis of the model, see ESI.w

Author contributions

Y.W. and R.F. designed research; Y.W. performed modeling;

Y.W., L.X.G. and R.F. analyzed the data; Y.W., L.X.G. and

R.F. wrote the paper.

Acknowledgements

We are grateful to Professor KathrynMiller-Jensen and Dr Qiong

Xue for valuable discussions. This work was supported by Yale

University New Faculty Startup Fund and the U.S. National

Cancer Institute Howard Temin Pathway to Independence Award

(NIH 4R00 CA136759-02, PI: R.F.). Y.W. is supported by the

Rudolph Anderson Postdoctoral Fellowship.

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